The diagram shows the pressure and volume of an ideal gas during one cycle of an engine. As
the gas proceeds from state 1 to state 2, it is heated at constant
pressure. It is then cooled at constant volume, until it reaches state
3. The gas is then cooled at constant pressure to state 4. Finally, the
gas is heated at constant volume until it returns to state 1.

Part A

Find , the work done by the gas as it expands from state 1 to state 2.

Part A.1

Part not displayed

Part A.2

Part not displayed

Express the work done in terms of and .

ANSWER:

=

9*p_0*V_0

Part B

Find , the work done by the gas as it cools from state 2 to state 3.

Hint B.1

Volume of the gas

Hint not displayed

Express your answer in terms of and .

ANSWER:

=

0

Part C

Find , the work done by the gas as it is compressed from state 3 to state 4.

Express your answer in terms of and .

ANSWER:

=

-3*p_0*V_0

Part D

Find , the work done by the gas as it is heated from state 4 to state 1.

Express your answer in terms of and .

ANSWER:

=

0

Part E

What is , the total work done by the gas during one cycle?

Express your answer in terms of and .

ANSWER:

=

6*p_0*V_0

Notice that the net work done by the gas during this cycle is equal to the area of the rectangle that appears in the pV (pressure-volume) diagram. (The width of this rectangle is , and its height is .) In other words, the net work done by this gas is equal to the net area under its pV curve. For a cycle, this is equivalent to the (signed) area enclosed by the cycle.

Part F

When the gas is in state 1, its temperature is . Find the temperature of the gas when it is in state 3. (Remember, this is an ideal gas.)